Previous research has indicated that ridge topology can be predicted by a model based on a principle of ridge length minimization. Results of direct tests of this “minimum spanning tree” postulate provide strong confirmation. In a sample of 230 ridge units from northeastern Kentucky, the observed topology minimized total ridge length in 174 cases (76%). The mean excess length for all ridge units was only 1.20%. Two other test areas, in California and British Columbia, produced similar results, although both have undergone considerable tectonic activity and one has been glaciated. Analysis of the geomorphometry of simple polyhedra indicates that a ridge configuration that minimizes total ridge length also minimizes the ratio of surface area to volume. This may provide a physical interpretation, heretofore lacking, for the minimum spanning tree postulate.